The solution of computational electromagnetics (CEM) problems involving periodic structures is of much interest to commercial as well as defense industries. Efficient and accurate CEM simulation enables, for example, an antenna designer to visualize a targeted antenna on a computer, providing in many cases more information than can ever be measured in a laboratory or in situ.
A commonly used technique for the analysis of arbitrarily large periodic structures is the electric field integral equation (EFIE) solved by the method of moments (MoM). EFIE-MoM is particularly well-suited for the analysis of planar structures. The MoM approach applies orthogonal expansions to translate the EFIE statement into a system of circuit-like simultaneous linear equations. Orthogonal sets of basis functions are used to expand the unknown current distribution Iz with invocation of boundary conditions, including the values of the electric field on the surface and in the feed gap, through the use of an inner product formulation. This system of equations is solved to yield the current's expansion coefficients. The original current distribution is then determined by introducing these coefficients back into the basis function expansion.
Solving for periodic structures such as infinite arrays using MoM, however, requires significant computational power. One approach makes use of periodic Green's functions (GFs) in two dimensions (i.e., an infinite double summation.) Ewald's transformations may be employed to accelerate computation of the GF, but this requires a high degree of complexity to implement.